Machine Learning Models for Sequential Conditional Independence Testing: Error Decomposition Explains Why Exchangeability Tests Win in Practice
Addressing the difficulty of incorporating machine learning models into log-optimal e-variable design for conditional independence testing, this work decomposes the error into null enlargement, approximation, and estimation error, explains why exchangeability tests with lower theoretical power can have higher power in practice, explores intermediate null hypotheses between model-X conditional independence and exchangeability to reduce these errors, and provides estimation error bounds accommodating triple robustness results.